Fly Off Screen
Play as Sonic (recommended), Miles, or Knuckles. Go to Zone 1 Act 1 and go to the area where the first loop is located. Stand on the sliver of land, then charge a spin dash for 20 seconds. Dash to the right and hold Down/Right. You will go down the hill (not getting all the rings). Eventually, you will go so fast that you will leave the screen. Sometimes it does not launch you off the cliff at the end.

Moon Zone
Collect all Chaos Emeralds by the end of the game, then play Sonic's X-Zone. Successfully complete the zone to unlock the bonus Moon Zone.